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A phase response curve (PRC) illustrates the transient change (phase response) in the cycle period of an oscillation induced by a perturbation as a function of the phase at which it is received. PRCs are used in various fields; examples of biological oscillations are the heartbeat, circadian rhythms , and the regular, repetitive firing observed ...
Magnitude response of a low pass filter with 6 dB per octave or 20 dB per decade roll-off. Measuring the frequency response typically involves exciting the system with an input signal and measuring the resulting output signal, calculating the frequency spectra of the two signals (for example, using the fast Fourier transform for discrete signals), and comparing the spectra to isolate the ...
It is usually a combination of a Bode magnitude plot, expressing the magnitude (usually in decibels) of the frequency response, and a Bode phase plot, expressing the phase shift. As originally conceived by Hendrik Wade Bode in the 1930s, the plot is an asymptotic approximation of the frequency response, using straight line segments .
The magnitude and phase components of () are plotted in the figure. But plots like these can also be generated by doing a discrete Fourier transform (DFT) of the impulse response. [B] And because of symmetry, filter design or viewing software often displays only the [0, π] region.
A minimum-phase system, whether discrete-time or continuous-time, has an additional useful property that the natural logarithm of the magnitude of the frequency response (the "gain" measured in nepers, which is proportional to dB) is related to the phase angle of the frequency response (measured in radians) by the Hilbert transform.
In this way, phase retrieval allows for the conversion of a diffraction pattern into an image without an optical lens. Using phase retrieval algorithms, it is possible to characterize complex optical systems and their aberrations. [6] For example, phase retrieval was used to diagnose and repair the flawed optics of the Hubble Space Telescope ...
The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
An example is for high-resolution audio in which the frequency response (magnitude and phase) for steady state signals (sum of sinusoids) is the primary filter requirement, while an unconstrained impulse response may cause unexpected degradation due to time spreading of transient signals. [2] [3]